How far can you see at sea? And when will you raise that light?

Further than you would guess, and it depends only on your height of eye. The distance to the visible horizon in nautical miles is 1.169 times the square root of your height of eye in feet. Standing on a small boat with your eyes 5 feet up, the horizon is 2.6 nm away. On a ship's bridge 70 feet up it is 9.8 nm. The relationship is a square root, so doubling your height buys you only about 41 per cent more distance — climbing the mast helps far less than people expect.

Because the atmosphere bends light downward around the curve of the earth. That terrestrial refraction pushes the visible horizon roughly 8 per cent beyond the geometric one, and Bowditch's 1.169 already contains it — you do not apply refraction separately. You will see 1.17, 2.07√m and 2.095√m quoted elsewhere; they come from slightly different refraction assumptions. This tool uses the Bowditch coefficient throughout and derives the metric form from it, so the two forms cannot disagree with each other.

Add two horizons: the light's distance to the horizon from its charted height, and your distance to the horizon from your height of eye. That sum is the light's geographic range — where it breaks your horizon. Then compare it with the light's luminous range, which is how far it is bright enough to be seen in the present visibility. You first sight the light at the lesser of the two. A powerful light beyond the horizon is still below it; a dim light well inside your horizon is still dim.

Nominal range is a brightness figure quoted at a standard 10 nautical miles of meteorological visibility, and it is what the US Coast Guard Light List usually prints. Luminous range is the same brightness question answered for the visibility you actually have — convert nominal to luminous with Bowditch's Luminous Range Diagram. Geographic range is pure geometry: two heights and the curve of the earth, with no reference to how bright the light is. Only the last of the three is what this calculator computes from heights.

Sighting a light and then lowering your height of eye — ducking, or stepping down a deck. If the light disappears and reappears when you return to your original height, it is exactly on your horizon, so you are at its geographic range. That gives you a distance off with no bearing, no radar and no fix, which is why it survives as a technique rather than just an exam sum.

Foreign publications often tabulate a light's geographic range for an assumed height of eye of 15 feet. If the printed figure looks like the geographic range rather than a brightness figure, reproduce it by entering 15 feet above, then swap in your real height of eye to get your own range. The Coast Guard Light List works differently — it lists nominal range, a brightness figure that needs no height-of-eye correction at all.